ProSoundWeb Community

Please login or register.

Login with username, password and session length
Advanced search  

Pages: [1]   Go Down

Author Topic: A quick demo on frequency, amplitude and phase I did today.  (Read 3584 times)

Jay Barracato

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 2025
  • Solomons, MD

Today I was setting up a demo to show the effect of changing frequency of a sinusoidal input on the amplitude and phase of the output. The expectation was that increasing the frequency should decrease the amplitude of the output and change the phase of the output.


Technically speaking, this is a sinusoidal steady state system, so with a input of vi(t) = Vi cos (wt) we would expect an output in the form vo(t) = A Vi cos (wt + phi) where A is a constant that is less than 1 and phi is the change in phase. (Not needed to understand the photos but for a LR series circuit A = R/sqrt(R^2 + w^2*L^2) and phi= arctan(-wL/R). Since the output cannot precede the input in time, the phi is chosen so the phase is lagging.


For the model, I used an input with a amplitude of 10V, a 1.0mH inductor, and a 1K resistor. The multisim model compares frequencies of 100kHz, 1MHz, and 10 MHz. For the real build, I dialed this back to a range from 50kHz to 500kHz.


The frequency effect on the amplitude and phase was clearly visible.


The real world point I was trying to convey is that any load can be modeled by a combination of its resistance, capacitance, and inductance (i.e. its impedance) and when using sinusoidal inputs we need to pay attention to both the amplitude and phase.

The first photo is the multisim model. The second is the breadboard, and the final three are the oscilloscope measurements comparing the purple input with the yellow output.
Logged
Jay Barracato

Tim Hite

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 1221
    • Bad Quail
Re: A quick demo on frequency, amplitude and phase I did today.
« Reply #1 on: May 15, 2019, 11:37:28 PM »

I should probably know this already. What are the variables w and t?
Logged
Bad Quail
Sound + Light + Image
Joshua Tree, California
Authorized Dealer for all this stuff

Jay Barracato

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 2025
  • Solomons, MD
Re: A quick demo on frequency, amplitude and phase I did today.
« Reply #2 on: May 15, 2019, 11:40:59 PM »

I should probably know this already. What are the variables w and t?
W (usually written as Omega) is the frequency in radians or 2pi(frequency in hz) and t is time in seconds.

Sent from my Moto Z (2) using Tapatalk

Logged
Jay Barracato

Frank Koenig

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 1318
  • Palo Alto, CA USA
Re: A quick demo on frequency, amplitude and phase I did today.
« Reply #3 on: May 17, 2019, 01:32:20 AM »

Try some lissajous figures as an alternative representation. Keep up the good work. --Frank
Logged
"Nature abhors a vacuum tube." -- John Pierce, Bell Labs

Jay Barracato

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 2025
  • Solomons, MD
Re: A quick demo on frequency, amplitude and phase I did today.
« Reply #4 on: May 17, 2019, 09:14:24 AM »

Try some lissajous figures as an alternative representation. Keep up the good work. --Frank

Had to look that one up. What Frank is referring to is treating the Input and Output functions of t as parametric equations and graphing them x vs y. Since the w is the same for both functions, the graph shows the phi as a repeating pattern. Since the ratio of the amplitudes is NOT =1, the pattern is an ellipse.


Photos go from relatively low (50Khz) to high (500 kHz) in frequency.
Logged
Jay Barracato

Tim Hite

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 1221
    • Bad Quail
Re: A quick demo on frequency, amplitude and phase I did today.
« Reply #5 on: May 17, 2019, 12:39:56 PM »

so as y/x approaches 1 you would expect a circle with diameter = phi?


Had to look that one up. What Frank is referring to is treating the Input and Output functions of t as parametric equations and graphing them x vs y. Since the w is the same for both functions, the graph shows the phi as a repeating pattern. Since the ratio of the amplitudes is NOT =1, the pattern is an ellipse.


Photos go from relatively low (50Khz) to high (500 kHz) in frequency.
Logged
Bad Quail
Sound + Light + Image
Joshua Tree, California
Authorized Dealer for all this stuff

Jay Barracato

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 2025
  • Solomons, MD
Re: A quick demo on frequency, amplitude and phase I did today.
« Reply #6 on: May 17, 2019, 05:10:54 PM »

so as y/x approaches 1 you would expect a circle with diameter = phi?
I am still trying to suss this out, but according to Wikipedia, the circle is when phi is 90 degrees. The aspect ratio of the ellipse, as phi goes from 0 to 90 degrees goes from a line, through ellipses, to a circle.

So it looks to me like the radius of the circle would be sqrt((Acos(wt))^2+(Bcos(wt+pi/2)^2)).

In other words, as a polar plot, we substituted cos(x+pi/2) for sin(x).

Sent from my Moto Z (2) using Tapatalk

Logged
Jay Barracato

Tim McCulloch

  • SR Forums
  • Hero Member
  • *
  • Offline Offline
  • Posts: 23736
  • Wichita, Kansas USA
Re: A quick demo on frequency, amplitude and phase I did today.
« Reply #7 on: May 20, 2019, 03:02:39 PM »

I am still trying to suss this out, but according to Wikipedia, the circle is when phi is 90 degrees. The aspect ratio of the ellipse, as phi goes from 0 to 90 degrees goes from a line, through ellipses, to a circle.

So it looks to me like the radius of the circle would be sqrt((Acos(wt))^2+(Bcos(wt+pi/2)^2)).

In other words, as a polar plot, we substituted cos(x+pi/2) for sin(x).

Sent from my Moto Z (2) using Tapatalk

Don Davis discusses tuning with Lissajous figures in the first edition of Sound System Engineering.  I think that was not included in subsequent editions.
Logged
"If you're passing on your way, from Palm Springs to L.A., Give a wave to good ol' Dave, Say hello to progress and goodbye to the Moonlight Motor Inn." - Steve Spurgin, Moonlight Motor Inn

Jay Barracato

  • Hero Member
  • *****
  • Offline Offline
  • Posts: 2025
  • Solomons, MD
Re: A quick demo on frequency, amplitude and phase I did today.
« Reply #8 on: May 20, 2019, 03:31:50 PM »

Don Davis discusses tuning with Lissajous figures in the first edition of Sound System Engineering.  I think that was not included in subsequent editions.
I can picture that, especially at the crossover frequency and the corner frequency of the filters.

I was already thinking of patching together a set of adapters to measure the filters with smaart. It would be interesting to look at them with the scope simultaneously.

Sent from my Moto Z (2) using Tapatalk

Logged
Jay Barracato

ProSoundWeb Community

Re: A quick demo on frequency, amplitude and phase I did today.
« Reply #8 on: May 20, 2019, 03:31:50 PM »


Pages: [1]   Go Up
 



Site Hosted By Ashdown Technologies, Inc.

Page created in 0.033 seconds with 24 queries.